Analytical Studies of Nonlinear Problems in Gravitational Field Theory
| Project/Area Number |
62540279
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Nagoya University |
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Principal Investigator |
TOMIMATSU Akira Faculty of Science, Nagoya University, 理学部, 教授 (10034612)
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| Co-Investigator(Kenkyū-buntansha) |
NOZAKI Kazuhiro Faculty of Science, Nagoya University, 理学部, 助教授 (00115619)
TANIUTI Tosiya Faculty of Science, Nagoya University, 理学部, 教授 (40022503)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Nonintegrable System / Gravitational Field Equation / Nonlinear Wave / Reductive Perturbation Method / Perturbation on Soliton / Singular Manifold Expansion / ブラックホール / アインシュタイン方程式 / 非線形重力波 / 非可積分系と近似法 / ソリトン |
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| Research Abstract |
This research project aimed to develop analytical methods in nonlinear mathematical physics and to apply them to nonlinear equations in gravitational field theory. The following results were obtained: 1.Developments of analytical methods.(1)By applying the reductive perturbation method to multi-dimensional wave propagation,it was shown that some nonlinear evolutional equations can be reduced to the Kadomtsev-Petviashvili aquation and the Zabolotskaya-Khokhlov equation.(2)Effects of nonintegrable perturbations on soliton systems were studied. It was found that a new stationary nonlinear wave which is different from the soliton can be excited by a weak external force,and a bound 2-soliton can split into individual solitons through a dispersive (or dissipative) perturbation.(3)Some nonintegrable equations were transformed into Hirota's bilinear form by a truncation of the singular manifold expansion,and the explicit solutions were derived.
2.Applications to gravitational field equations.(1)By applying the method of characteristics,a propagation character of nonlinear waves in a string-induced gravity theory was studied. The new black-hole solution which has a thermodynamic property different from the Schwarzschild solution was also derived.(2)By using soliton solutions of the cylindlical Einstein equations,it was shown that the gravitational Faraday rotation due to a nonlinear interaction of gravitational waves occurs effectively. (3)Based on the perturbation theory for the Schwarzschild solution,the ploblem of a head-on collision of two black holes was studied. The initial data were constructed,and the subsequent time-evolution of gravitational field was calculated.The emission of pulse-like waves and the increase increase of the area of black holes were explicitly shown. Further developments of analytical methods in nonintegrable gravitational field equations remain to future investigations.
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Report
(3 results)
Research Products
(33 results)
